A practical and accessible introduction to the bootstrap methodnewly revised and updated Over the past decade, the application of bootstrap methods to new areas of study has expanded, resulting in theoretical and applied advances across various fields. Bootstrap Methods, Second Edition is a highly approachable guide to the multidisciplinary, real-world uses of bootstrapping and is ideal for readers who have a professional interest in its methods, but are without an advanced background in mathematics. Updated to reflect current techniques and the most up-to-date work on the topic, the Second Edition features: The addition of a second, extended bibliography devoted solely to publications from 19992007, which is a valuable collection of references on the latest research in the field A discussion of the new areas of applicability for bootstrap methods, including use in the pharmaceutical industry for estimating individual and population bioequivalence in clinical trials A revised chapter on when and why bootstrap fails and remedies for overcoming these drawbacks Added coverage on regression, censored data applications, P-value adjustment, ratio estimators, and missing data New examples and illustrations as well as extensive historical notes at the end of each chapter With a strong focus on application, detailed explanations of methodology, and complete coverage of modern developments in the field, Bootstrap Methods, Second Edition is an indispensable reference for applied statisticians, engineers, scientists, clinicians, and other practitioners who regularly use statistical methods in research. It is also suitable as a supplementary text

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We characterize in geometric terms the zero sets of holomorphic functions$f$in the bidisk such that log |$f$|∈$L$^{$p$}($D$^{2}) for 1<$p$<∞.

Let$I$be a union of finitely many closed intervals in [−1, 0). Let$I$^{↞}be a single interval of the form [−1, −a] chosen to have the same logarithmic length as$I$. Let$D$be the unit disc. Then, Beurling [8] has shown that the harmonic measure of the circle ∂$D$at the origin in the slit disc$D$/$I$is increased if$I$is replaced by$I$^{↞}. We prove a number of cognate results and extensions. For instance, we show that Beurling's result remains true if the intervals in$I$are not just one-dimensional, but if they in fact constitute polar rectangles centred on the negative real axis and having some fixed constant angular width. In doing this, we obtain a new proof of Beurling's result. We also discuss a conjecture of Matheson and Pruss [25] and some other open problems.